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Research Seminars: Graduate Student Colloquium

Fall 2022

Time & Location: All talks are on Tuesdays in Stanley Thomas 316 at 5:00 PM unless otherwise noted.
Organizer: Nathaniel Vaduthala


August 30

Title: The transportation method in Concentration Inequalities.
Ying Bi | Tulane University

Abstract: The Concentration inequalities are widely used in Probability Theory, Statistical mechanics, information theory and many other fields. Among all the methods in proving such inequalities, the entropy method performs especially well when dealing with suprema of empirical processes, but often faces difficulties when deal with left tail. However, the transportation method provided by Prof Marton in the mid 1990s is more efficient for left tail. We will see the basic idea of proving inequalities based on cost function and the induction spirit in this talk with several examples at the end. Some references will also shown in the appendix for further reading.

Time: 5:00pm
Location:  Stanley Thomas 316


September 6

Title: Projection Method and Linear Algebra
Sang-Eun Lee - Tulane University

Abstract: Due to the millennium problem for the global existence and regularity of the 3D Navier-Stokes equations for the viscous and incompressible flow, we cannot obtain an explicit solution to the system of fluid equations. So, we rely on the computational method to describe and understand fluid motion. There are a few numerical methods to find an approximated solution, but due to the massiveness of the matrix size, people have tried to find to reduce the computational cost of the methods. A well-known method to find the numerical solution of fluid motion is called the projection method, due to Alexandre Chorin. This talk briefly describes the fluid-structure and discusses some linear algebraic skills in each scenario.

Time: 5:00pm
Location:  Stanley Thomas 316


September 17

Title: Hilbert's 17th Problem
Naufil Sakran - Tulane University

Abstract: Hilbert proposed 23 questions in 1900 at the conference of the International Congress of Mathematics. Answers to these questions have high influence in Modern Mathematics. Hilbert's 17 problem asks about the minimal requirement to a polynomial so that it has representation as sum of squares. The talk will focus on answering the question. Finally, we will discuss open problems regarding it.

Time: 5:00pm
Location:  Stanley Thomas 316


September 20

Title: Shor's Algorithm and Quantum Supremac
Rubaiyat Islam - Tulane University

Abstract: Shor's algorithm is a quantum computing algorithm which shows that a programmable quantum computer can factor integers in polynomial time. Currently used important cryptographic algorithms critically depend on the fact that prime factorization of large numbers with classical algorithms takes a long time. A factoring problem can be turned into a period finding problem and the quantum part of Shor's algorithm significantly speeds up this period finding step. In this talk, we will look at the relation between the two problems, what gives quantum advantage and try to see some output from an actual quantum computer.

Time: 5:00pm
Location:  Stanley Thomas 316


September 30

Title: The Mathematics of Musical Tuning
Peter Marcus - Tulane University

Abstract: Designers of musical instruments need to decide how they will be tuned, meaning what pitches the instrument can produce. Today the most common tuning system by far is 12-tone equal temperament, but how was this chosen and why is it so popular? I will give a brief history of European tuning systems and dive into the math behind them.

Location:  Stanley Thomas 316


December 9
Last Day Of Class